Lab 4 Results
Eric Kruger
October 18, 2015
Questions to answer
Looking over the data I did notice some NaN largely because the optical values were too large. This value placed them just outside the standard curve. It appears from the data that optical densities above 2.03 are recorded as NaN. This corresponds to a testosterone concentration of approx. 21 pg/ml. I did notice one issue, which was that when trying to determine the fitted concentration if one of the duplicate values were too high then it would just provide the output of NaN for the average. A solution to this problem would be to simply take one of the values and not perform the average function. This appears to be what was done for my data when it was compiled. If both results in duplicate came out of NaN and they were in duplicate then one could just take the highest value on the standard curve i.e. above 2.03 replace this with approx. 10 of pg/ml–the last value on the standard curve.
I would look at the optical density. If the optical density is high i.e. above 2.03 then the results produce a NaN and this would indicate that there is a small amount of testosterone in the sample. If the optical density is small i.e. above 0.19 then there is a large concentration in the sample i.e. above 5000 pg/ml.
The inter-assay CV is \(16.39\)%.
The intra-assay CV for controls were \(28.9\)% and \(21.25\)% for control 1 and 2, respectively.
I don’t see any extreme outliers in my particular data. There was only one particular case for my fifth subject were the duplicate optical densities severely disagreed with each other. This was the case with both the pre and post observations pre (2.22 and 1.86) and post (2.26 and 1.69) for sample 1 and 2 respectively. This indicates that there was likely human error in the procedures related to pipetting. Other causes of outliers might be if the subject did not follow the instructions for taking the sample, inappropriate storage techniques (i.e. no freezing) or other contamination of the sample.
Is there an interaction between males and females and win or lose condition for difference scores?
Anova Table (Type III tests)
Response: T.d
Sum Sq Df F value Pr(>F)
(Intercept) 0.16876 1 2.9091 0.09383 .
MF 0.04097 1 0.7062 0.40442
Condition 0.12122 1 2.0895 0.15409
MF:Condition 0.13930 1 2.4012 0.12708
Residuals 3.13271 54
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
- I wanted to examine if there was an interaction in the difference score between the factors of sex and win/lose. I used a 2x2 ANOVA on the difference score (log of the testosterone concentration). My conclusion is that there is not a significant interaction, however it does appear to be trending towards significance I wanted to check my assumption of normality so I also included a graph of the residuals. While the graph does appear to approximate the normal distribution there is a slight left skew.
6.Do males differ than females in pre, post and difference scores?
Welch Two Sample t-test
data: T.pre by MF
t = -6.784, df = 45.33, p-value = 2.06e-08
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.5360086 -0.2906352
sample estimates:
mean in group F mean in group M
1.229805 1.643127
Welch Two Sample t-test
data: T.post by MF
t = -5.4608, df = 33.249, p-value = 4.627e-06
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.5796986 -0.2650601
sample estimates:
mean in group F mean in group M
1.286615 1.708995
Welch Two Sample t-test
data: T.d by MF
t = -0.1323, df = 36.24, p-value = 0.8955
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.1478754 0.1297605
sample estimates:
mean in group F mean in group M
0.05680987 0.06586733 - Males and females are significantly different in their pre and post concentrations of testosterone–males being higher than females. Again the data is log transformed to account for the non-normality. No significant differences were found in the males difference scores compared to female difference scores from pre to post.
- Is there a pattern across times of day
Call:
lm(formula = T ~ Time, data = data)
Residuals:
Min 1Q Median 3Q Max
-34.931 -22.660 -6.934 14.959 110.779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.643e+06 1.497e+07 0.377 0.707
Time 9.078e-05 2.408e-04 0.377 0.707
Residual standard error: 30.61 on 102 degrees of freedom
(8 observations deleted due to missingness)
Multiple R-squared: 0.001391, Adjusted R-squared: -0.008399
F-statistic: 0.1421 on 1 and 102 DF, p-value: 0.707- There is not a significant difference across times of day and the testosterone level as the adjusted R^2 is small and the p-value does not reach significance
Call:
lm(formula = T.log ~ Time, data = dataMW)
Residual standard error: 0.2419 on 17 degrees of freedom
Multiple R-squared: 0.6433, Adjusted R-squared: 0.2236
F-statistic: 1.533 on 20 and 17 DF, p-value: 0.1889
####
Call:
lm(formula = T.log ~ Time, data = dataML)
Residual standard error: 0.1291 on 15 degrees of freedom
Multiple R-squared: 0.8586, Adjusted R-squared: 0.6513
F-statistic: 4.141 on 22 and 15 DF, p-value: 0.003338
####
Call:
lm(formula = T.log ~ Time, data = dataWW)
Residual standard error: 0.4148 on 1 degrees of freedom
Multiple R-squared: 0.7889, Adjusted R-squared: -1.745
F-statistic: 0.3114 on 12 and 1 DF, p-value: 0.9017
####
Call:
lm(formula = T.log ~ Time, data = dataWL)
Residual standard error: 0.1987 on 6 degrees of freedom
Multiple R-squared: 0.8486, Adjusted R-squared: 0.3691
F-statistic: 1.77 on 19 and 6 DF, p-value: 0.2471- When examining the regression lines separately only the condition where males lose shows a significant difference in testosterone scores across time. It might be tempting to conclude that this means that if males lose in the evening they show a decrease in testosterone. However, our test only asks if the \(\beta\) coefficient is different than zero not if the \(\beta\) for winning is different than \(\beta\) for losing. Even though the trend lines make it appear as if they are different we cannot make a statement of significance about the difference between these two regression coefficients.
- Do Pre and Post Scores Differ?
One Sample t-test
data: T.d
t = 1.9925, df = 57, p-value = 0.05111
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
-0.0003139927 0.1258021250
sample estimates:
mean of x
0.06274407 - I just performed a one sample t test on the difference score which is the same as two sample paired t test. I concluded that because our p-value is not below \(\alpha\) that we have insufficient evidence to reject the null hypothesis and that the pre and post scores means are not significantly different. However it is close with a \(p-value = 0.051\).
- Does testosterone differ across conditions (winning and losing)
Welch Two Sample t-test
data: T.pre by Condition
t = -1.6856, df = 55.737, p-value = 0.09747
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.28794047 0.02481051
sample estimates:
mean in group Lose mean in group Win
1.441625 1.573190
Welch Two Sample t-test
data: T.post by Condition
t = -1.2945, df = 50.886, p-value = 0.2014
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.2904541 0.0627358
sample estimates:
mean in group Lose mean in group Win
1.512306 1.626165
Welch Two Sample t-test
data: T.d by Condition
t = 0.27321, df = 49.835, p-value = 0.7858
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.1124712 0.1478829
sample estimates:
mean in group Lose mean in group Win
0.07068116 0.05297533 - No significant differences were found in scores in testosterone concentration in those who won and lost, pre, post or the difference between pre and post.
